From 41061d0dc42afe19b520059f36a98d4ec870825f Mon Sep 17 00:00:00 2001 From: Matej Kosik Date: Thu, 29 Oct 2015 09:05:48 +0100 Subject: CLEANUP PROPOSITION: Duplicate information was removed and replaced with a reference to the corresponding chapter. --- doc/refman/RefMan-cic.tex | 39 +++------------------------------------ 1 file changed, 3 insertions(+), 36 deletions(-) diff --git a/doc/refman/RefMan-cic.tex b/doc/refman/RefMan-cic.tex index 7986648fb9..c481b3adba 100644 --- a/doc/refman/RefMan-cic.tex +++ b/doc/refman/RefMan-cic.tex @@ -5,42 +5,9 @@ \index{Calculus of Inductive Constructions}} The underlying formal language of {\Coq} is a {\em Calculus of - Inductive Constructions} (\CIC) whose inference rules are presented in -this chapter. - -The {\CIC} implemented in {\Coq} -takes its name from Coquand and Paulin's {\em Calculus of - Inductive Constructions}~\cite{CoPa89} which itself extends -Coquand-Huet's {\em Calculus of - Constructions}~\cite{CoHu85a,CoHu85b,CoHu86,Coq85} with a universe -hierarchy~\cite{Coq86,Luo90,Hue88b} and a generic presentation of -inductive types à la Martin-L\"of~\cite{MaL84,Dyb91}. First implemented in -{\Coq} version 5.0, it incorporated coinductive -types~\cite{Coquand93,Gim96} from {\Coq} version 5.10. It -progressively extended with various new features such as local -definitions (since {\Coq} version 7.0), universe polymorphism (since -{\Coq} version 8.1 for inductive types and version 8.5 for full -polymorphism), recursively non-uniform parameters (since {\Coq} version 8.1), -some $\eta$-rules (for dependent product in {\Coq} -version 8.4, for record types in {\Coq} version 8.5), and other -refinements in the expressiveness of fixpoints and inductive types. -Up to version 7.4, the {\CIC} implemented in {\Coq} -had an impredicative sort {\Set}. Since {\Coq} version 8.0, the sort -{\Set} is predicative by default, with an option to make it -impredicative (see Section~\ref{impredicativity}). - -The reader seeking a background on the Calculus of Inductive -Constructions may read several papers. In addition to the references given above, Giménez and Castéran~\cite{GimCas05} -provide -an introduction to inductive and co-inductive definitions in {\Coq}. In -their book~\cite{CoqArt}, Bertot and Castéran give a -description of the \CIC{} based on numerous practical examples. -Barras~\cite{Bar99}, Werner~\cite{Wer94} and -Paulin-Mohring~\cite{Moh97} are dealing with -Inductive Definitions. The {\CIC} is a -formulation of type theory including the possibility of inductive -constructions, Barendregt~\cite{Bar91} studies the modern form of type -theory. +Inductive Constructions} (\CIC) whose inference rules are presented in +this chapter. The history of this formalism as well as pointers to related work +are provided in a separate chapter; see {\em Credits}. \section[The terms]{The terms\label{Terms}} -- cgit v1.2.3